2. Winter 2011
UCSD: Physics 121; 2011
2
Why Vacuum?
• Anything cryogenic (or just very cold) needs to get rid
of the air
– eliminate thermal convection; avoid liquefying air
• Atomic physics experiments must get rid of
confounding air particles
– eliminate collisions
• Sensitive torsion balance experiments must not be
subject to air
– buffeting, viscous drag, etc. are problems
• Surface/materials physics must operate in pure
environment
– e.g., control deposition of atomic species one layer at a time
3. Winter 2011
UCSD: Physics 121; 2011
3
Measures of pressure
• The “proper” unit of measure for pressure is Pascals
(Pa), or N·m-2
• Most vacuum systems use Torr instead
– based on mm of Hg
• Atmospheric pressure is:
– 760 Torr
– 101325 Pa
– 1013 mbar
– 14.7 psi
• So 1 Torr is 133 Pa, 1.33 mbar; roughly one milli-
atmosphere
4. Winter 2011
UCSD: Physics 121; 2011
4
Properties of a vacuum
Vacuum Pressure
(torr)
Number
Density (m-3)
M.F.P.
(m)
Surface Collision
Freq. (m-2·s-1)
Monolayer
Formation
Time (s)
Atmosphere 760 2.71025 7108 31027 3.310-9
Rough 103 3.51019 0.05 41021 2.510-3
High 106 3.51016 50 41018 2.5
Very high 109 3.51013 50103 41015 2.5103
Ultrahigh 1012 3.51010 50106 41012 2.5106
5. Winter 2011
UCSD: Physics 121; 2011
5
Kinetic Theory
• The particles of gas are moving randomly, each with
a unique velocity, but following the Maxwell
Boltzmann distribution:
• The average speed is:
• With the molecular weight of air around 29 g/mole
(~75% N2 @ 28; ~25% O2 @ 32), 293 K:
– m = 291.6710-27 kg
– <v> = 461 m/s
– note same ballpark as speed of sound (345 m/s)
6. Winter 2011
UCSD: Physics 121; 2011
6
Mean Free Path
• The mean free path is the typical distance traveled
before colliding with another air molecule
• Treat molecules as spheres with radius, r
• If (the center of) another molecule comes within 2r of
the path of a select molecule:
• Each molecule sweeps out cylinder of volume:
V = 4r2vt
– in time t at velocity v
• If the volume density of air molecules is n (e.g., m3):
– the number of collisions in time t is
notZ = 4nr2vt
• Correcting for relative molecular speeds, and
expressing as collisions per unit time, we have:
7. Winter 2011
UCSD: Physics 121; 2011
7
Mean Free Path, cont.
• Now that we have the collision frequency, Z, we can
get the average distance between collisions as:
= v/Z
• So that
• For air molecules, r 1.7510-10 m
• So 6.8108 m = 68 nm at atmospheric pressure
• Note that mean free path is inversely proportional to
the number density, which is itself proportional to
pressure
• So we can make a rule for = (5 cm)/(P in mtorr)
8. Winter 2011
UCSD: Physics 121; 2011
8
Relevance of Mean Free Path
• Mean free path is related to thermal conduction of air
– if the mean free path is shorter than distance from hot to cold
surface, there is a collisional (conductive) heat path between
the two
• Once the mean free path is comparable to the size of
the vessel, the paths are ballistic
– collisions cease to be important
• Though not related in a 1:1 way, one also cares
about transition from bulk behavior to molecular
behavior
– above 100 mTorr (about 0.00013 atm), air is still collisionally
dominated (viscous)
• is about 0.5 mm at this point
– below 100 mTorr, gas is molecular, and flow is statistical
rather than viscous (bulk air no longer pushes on bulk air)
9. Winter 2011
UCSD: Physics 121; 2011
9
Gas Flow Rates
• At some aperture (say pump port on vessel), the flow
rate is
S = dV/dt (liters per second)
• A pump is rated at a flow rate:
Sp = dV/dt at pump inlet
• The mass rate through the aperture is just:
Q = PS (Torr liter per second)
• And finally, the ability of a tube or network to conduct
gas is
C (in liters per second)
• such that
Q = (P1 P2)C
10. Winter 2011
UCSD: Physics 121; 2011
10
Evacuation Rate
• What you care about is evacuation rate of vessel
• S = Q/P1
• but pump has Sp = Q/P2
• Q is constant (conservation of mass)
• Q = (P1 P2)C, from which you can get:
1/S = 1/Sp + 1/C
• So the net flow looks like the “parallel” combination of
the pump and the tube:
– the more restrictive will dominate
• Usually, the tube is the restriction
– example in book has 100 l/s pump connected to tube 2.5 cm
in diameter, 10 cm long, resulting in flow of 16 l/s
– pump capacity diminished by factor of 6!
P1
P2
Q
Q
Q
C
pump: Sp
11. Winter 2011
UCSD: Physics 121; 2011
11
Tube Conductance
• For air at 293 K:
• In bulk behavior (> 100 mTorr):
C = 180PD4/L (liters per second)
– D, the diameter, and L, the length are in cm; P in Torr
– note the strong dependence on diameter!
– example: 1 m long tube 5 cm in diameter at 1 Torr:
• allows 1125 liters per second
• In molecular behavior (< 100 mTorr):
C = 12D3/L
– now cube of D
– same example, at 1 mTorr:
• allows 0.1 liters per second (much reduced!)
12. Winter 2011
UCSD: Physics 121; 2011
12
Pump-down time
• Longer than you wish
– Viscous air removed quickly, then long slow process to
remove rest
– to go from pressure P0 to P, takes t = (V/S)ln(P0/P)
– note logarithmic performance
13. Winter 2011
UCSD: Physics 121; 2011
13
Mechanical Pumps
• Form of “positive
displacement pump”
• For “roughing,” or getting the
the bulk of the air out, one
uses mechanical pumps
– usually rotary oil-sealed
pumps
– these give out at ~ 1–10
mTorr
• A blade sweeps along the
walls of a cylinder, pushing
air from the inlet to the
exhaust
• Oil forms the seal between
blade and wall
14. Winter 2011
UCSD: Physics 121; 2011
14
Lobe Injection Pumps
• Can move air very rapidly
• Often no oil seal
• Compression ratio not as
good
15. Winter 2011
UCSD: Physics 121; 2011
15
Turbomolecular pumps
• After roughing, one often goes
to a turbo-pump
– a fast (24,000 RPM) blade
achieves a speed comparable
to the molecular speed
– molecules are mechanically
deflected downward
• Work only in molecular regime
– use after roughing pump is
spent (< 100 mTorr)
• Usually keep roughing pump on
exhaust
16. Winter 2011
UCSD: Physics 121; 2011
16
Cryopumping
• A cold surface condenses volatiles (water, oil, etc.)
and even air particles if sufficient nooks and crannies
exist
– a dessicant, or getter, traps particles of gas in cold
molecular-sized “caves”
• Put the getter in the coldest spot
– helps guarantee this is where particles trap: don’t want
condensation on critical parts
– when cryogen added, getter gets cold first
• Essentially “pumps” remaining gas, and even
continued outgassing
• Called cryo-pumping
17. Winter 2011
UCSD: Physics 121; 2011
17
Ion Pump
• Ionize gas molecules, deposit ions on
chemically active surface, removed by
chemisorption
• Best use is for Ultra-High Vacuum
applications (10-11 Torr)
• Current is proportional to pressure (pump is
also a pressure gauge)
• No moving parts, but efficient only at very
low pressures
slide courtesy O. Shpyrko
18. Winter 2011
UCSD: Physics 121; 2011
18
Residual Gas Analyzer
(mass spectrometer)
• Electronic “nose”, sniffing inside the
chamber
• Can detect partial pressure down to
10-14 Torr
• Useful as a He leak-detector
• Measures mass-to-charge ratio by
ionizing a molecule and accelerating it
in EM field
slide courtesy O. Shpyrko
19. Winter 2011
UCSD: Physics 121; 2011
19
Example of RGA spectra, He:Ne mixture 10:1
slide courtesy O. Shpyrko
20. Winter 2011
UCSD: Physics 121; 2011
20
Typical problems in achieving UHV:
• Actual Leaks (valves, windows)
• Slow pump-down times
• “Virtual” leaks
• Outgassing – bulk and surfaces
Solutions:
• Leak-testing
• Re-design of vacuum chamber
• Bake-out
• Cryopumping
slide courtesy O. Shpyrko
21. Winter 2011
UCSD: Physics 121; 2011
21
Dewars
• Evacuating the region
between the cold/hot wall
and the ambient wall
eliminates convection and
direct air conduction
• Some conduction over the
lip, through material
– minimized by making thin
and out of thermally non-
conductive material
• Radiation is left, but
suppressed by making all
surfaces low emissivity
(shiny)
• Heat paths cut holds
temperature of fluid
22. Winter 2011
UCSD: Physics 121; 2011
22
Liquid Nitrogen Dewar
• Many Dewars are passively cooled via liquid nitrogen, at 77 K
• A bath of LN2 is in good thermal contact with the “inner shield” of
the dewar
• The connection to the outer shield, or pressure vessel, is
thermally weak (though mechanically strong)
– G-10 fiberglass is good for this purpose
• Ordinary radiative coupling of (Th
4 Tc
4) = 415 W/m2 is cut to a
few W/m2
– Gold plating or aluminized mylar are often good choices
– bare aluminum has 0.04
– gold is maybe 0.01
– aluminized mylar wrapped in many layered sheets is common (MLI:
multi-layer insulation)
– MLI wants to be punctured so-as not to make gas traps: makes for
slooooow pumping
23. Winter 2011
UCSD: Physics 121; 2011
23
Dewar Construction
• Cryogen is isolated from
warm metal via G-10
– but in good thermal contact
with inner shield
• Metal joints welded
• Inner shield gold-coated or
wrapped in MLI to cut
radiation
• Windows have holes cut into
shields, with vacuum-tight
clear window attached to
outside
• Can put another, nested,
inner-inner shield hosting
liquid helium stage
vacuum
port
cryogen
port
pressure vessel/outer shield
inner shield
cryogen (LN2)
tank
perforated G-10
cylinder
science apparatus
24. Winter 2011
UCSD: Physics 121; 2011
24
Cryogen Lifetime
• Note that LN2 in a bucket in a room doesn’t go “poof”
into gas
– holds itself at 77 K: does not creep to 77.1K and all
evaporate
– due to finite “heat of vaporization”
• LN2 is 5.57 kJ/mole, 0.81 g/mL, 28 g/mol 161 J/mL
• L4He is 0.0829 kJ/mol, 0.125 g/mL, 4 g/mol 2.6 J/mL
• H2O is 40.65 kJ/mol, 1.0 g/mL, 18 g/mol 2260 J/mL
• If you can cut the thermal load on the inner shield to
10 W, one liter of cryogen would last
– 16,000 s 4.5 hours for LN2
– 260 s 4 minutes for LHe
25. Winter 2011
UCSD: Physics 121; 2011
25
Nested Shields
• LHe is expensive, thus the need for nested shielding
• Radiative load onto He stage much reduced if
surrounded by 77 K instead of 293 K
– (2934 44) = 418 W/m2
– (774 44) = 2.0 W/m2
– so over 200 times less load for same emissivity
– instead of a liter lasting 4 minutes, now it’s 15 hours!
– based on 10 W load for same configuration at LN2
26. Winter 2011
UCSD: Physics 121; 2011
26
Coolest place on earth:
• Antarctica -89 °C, or 183K
• San Diego: Dilution fridges
Mayer Hall (Maple, Goodkind), NSB (Butov) ~300 mK
• Cambridge, MA: Sub-500 picoKelvin achieved in
Ketterle group at MIT
See “Cooling Bose-Einstein Condensates Below 500 Picokelvin”
Science 301, 5639 pp. 1513 - 1515 (2003)
slide courtesy O. Shpyrko
